Draft version November 7, 2014
Preprint typeset using LATEX style emulateapj v. 5/2/11
THE EFFECTS OF INITIAL ABUNDANCES ON NITROGEN IN PROTOPLANETARY DISKS
Kamber R. Schwarz and Edwin A. Bergin
arXiv:1411.1403v1 [astro-ph.SR] 5 Nov 2014
Department of Astronomy, University of Michigan, 500 Church Street, Ann Arbor, MI 48109, USA
Draft version November 7, 2014
ABSTRACT
The dominant form of nitrogen provided to most solar system bodies is currently unknown, though
available measurements show that the detected nitrogen in solar system rocks and ices is depleted
with respect to solar abundances and the interstellar medium. We use a detailed chemical/physical
model of the chemical evolution of a protoplanetary disk to explore the evolution and abundance
of nitrogen-bearing molecules. Based on this model we analyze how initial chemical abundances,
provided as either gas or ice during the early stages of disk formation, influence which species become
the dominant nitrogen bearers at later stages. We find that a disk with the majority of its initial
nitrogen in either atomic or molecular nitrogen is later dominated by atomic and molecular nitrogen
as well as NH3 and HCN ices, where the dominant species varies with disk radius. When nitrogen
is initially in gaseous ammonia, it later becomes trapped in ammonia ice except in the outer disk
where atomic nitrogen dominates. For a disk with the initial nitrogen in the form of ammonia ice
the nitrogen remains trapped in the ice as NH3 at later stages. The model in which most of the
initial nitrogen is placed in atomic N best matches the ammonia abundances observed in comets.
Furthermore the initial state of nitrogen influences the abundance of N2 H+ , which has been detected
in protoplanetary disks. Strong N2 H+ emission is found to be indicative of an N2 abundance greater
than nN2 /nH2 > 10−6 , in addition to tracing the CO snow line. Our models also indicate that NO is
potentially detectable, with lower N gas abundances leading to higher NO abundances.
1. INTRODUCTION
Most solar system bodies are depleted in nitrogen relative to the Sun and the ISM. Pontoppidan et al. (2014)
compare the CNO abundances in various solar system
bodies relative to silicon. Comets Halley and Hale-Bopp,
which likely formed in the outer disk (R > 10 AU), where
there is thought to be less chemical reprocessing, are depleted in nitrogen by less than an order of magnitude
with respect to solar values. In contrast the nitrogen
content of meteorites is between one and three orders
of magnitude below the amount of nitrogen that was
available, as traced by the Sun (Asplund et al. 2009).
In fact, comets and meteorites exhibit greater depletion
in nitrogen than in other volatiles such as oxygen and
carbon (Pontoppidan et al. 2014). In this context the
Earth is extremely depleted in nitrogen with an abundance ratio more than five orders of magnitude below
the solar abundance. Most of the known nitrogen resides in the atmosphere in the form of N2 , however, it
is possible that much of Earth’s nitrogen was locked in
its interior (Roskosz et al. 2013). The 15 N/14 N ratio
of the terrestrial surface, which includes the atmosphere
and oceans, as well as the crust, agrees with that of
chondrites, suggesting that both the Earth’s surface and
meteorites obtained their nitrogen from the same reservoir (Marty 2012). It remains unclear what the dominant nitrogen-bearing species was upon delivery to the
young Earth, whether it was carried by organics in meteorites, N2 from the solar nebular gas, or NH3 /organics
in cometary bodies (Epstein et al. 1987; Wyckoff et al.
1991; Owen et al. 2001; Kawakita et al. 2007).
The Cronian satellites Titan and Enceladus both show
evidence of rich N2 atmospheres (Niemann et al. 2005;
Waite et al. 2006). Isotopic abundances in Titan’s atmo-
sphere were measured by the Huygens probe and the low
36
Ar/14 N ratio along with the absence of detectable of
38
Ar, Kr and Xe provides circumstantial evidence that
Titan first received its nitrogen in a less volatile form,
such as NH3 (Niemann et al. 2005). The nitrogen could
later be converted to the more volatile N2 , possibly by
impacts during the period of late heavy bombardment
(Sekine et al. 2011).
Which nitrogen-bearing molecules end up in solar system bodies depends on the chemical composition of the
protoplanetary disk at the time of planetesimal formation. In this paper we show that the dominant bearer
of nitrogen is highly dependent on initial chemical abundances. There continues to be some uncertainty in regards to the nitrogen partitioning in dense molecular prestellar cores, which represent the initial conditions. This
uncertainty stems from the difficulty of detecting many
of the most probable nitrogen reservoirs: N, N2 , and
nitrogen-bearing ices. N and N2 are not directly observable in the dense ISM. Instead their abundances must
be inferred from observations of trace molecules such as
N2 H+ , which is a reaction product of N2 . NH3 ice abundances are derived from absorption features. However,
the measured NH3 ice abundances are uncertain due to
the blending of particular absorption features with those
of water and silicates (Öberg et al. 2011a).
Spectroscopic observations of ices toward low-mass
young stellar objects as part of the Spitzer “Cores to
Disks” program find that on average 10% of the total nitrogen is contained in known ices, primarily NH3 , NH+
4,
and XCN (OCN− ), though in some sources the percentage is as high as 34% (Öberg et al. 2011a). The remaining nitrogen is posited to reside in the gas phase
as either atomic N or N2 . Womack et al. (1992) esti-
2
mate N2 abundances in multiple dense molecular cores
using observations of N2 H+ . They find an average fractional abundance of 4×10−6 with respect to H2 , or 6%
of the total nitrogen reservoir assuming solar abundances
(Asplund et al. 2009). Maret et al. (2006) find the gas
phase nitrogen to be primarily in atomic as opposed to
molecular nitrogen for the prestellar core B68, though
based on their models the main nitrogen-bearing species
is NH3 ice. Similarly, Daranlot et al. (2012) conclude
that 45% of the total elemental nitrogen in dense clouds
is in the form of NH3 ices on grains, though the abundances they predict are larger than those observed. Le
Gal et al. (2014) modeled the gas phase nitrogen chemistry in dark clouds. Starting with nitrogen all in gas
phase N they find that once a steady state is reached the
dense core contains equal abundances of N and N2 with
a small fraction of the initial nitrogen in other species.
NH3 has long been a tracer of dense cores (e.g. Benson
& Myers 1989). Using detections of NH3 inverse transitions toward five starless cores, Tafalla et al. (2002)
calculated NH3 gas abundances ranging 4.0 × 10−9 to
1.0 × 10−8 with respect to H2 . NH3 gas has also been observed in absorption several thousand AU from the Class
0 protostar IRAS 16293-2422 with an abundance relative
to H2 of ≈ 3.6 × 10−7 − 6.5 × 10−7 (Hily-Blant et al.
2010). Finally, Le Gal et al. (2014) find that the steady
state abundances of nitrogen hydrides in their chemical
model were in good agreement with those observed toward IRAS 16293-2422. In sum, in prestellar cores, gas
phase NH3 is clearly not a major nitrogen reservoir, however as discussed earlier there is a significant amount of
NH3 potentially present in the ices. Visser et al. (2011)
modeled the chemical evolution of a collapsing protostar
from a pre-stellar core to a disk, finding that the disk
begins with most of the nitrogen in gas phase N2 with
minor contributions from N, NH3 , and NO.
Despite detections in these earlier stages of star formation there are currently no published detections of NH3
gas in protoplanetary disks, though upper limits exist for
several T Tauri stars in the near-infrared (Salyk et al.
2011; Mandell et al. 2012). However, both CN and HCN
have been detected in multiple protoplanetary disks (e.g.
Öberg et al. 2011b; Guilloteau et al. 2013) and resolved
N2 H+ emission is seen in the T Tauri system TW Hya
(Qi et al. 2013) while unresolved emission is seen toward
several more systems (Dutrey et al. 2007; Öberg et al.
2010, 2011b).
Thus a variety of potential initial distributions of the
total nitrogen reservoir could be provided to the forming disk. It is possible that a substantial fraction of the
nitrogen could be in the form of N gas, N2 gas, or NH3
ices. Alternatively, if the source is warm enough during
collapse, a significant amount of NH3 could be provided
to the disk as NH3 gas. In this paper we perform simulations of the disk chemistry in which we make four
different initial abundance assumptions: (1) most of the
nitrogen is in atomic form; (2) most of the nitrogen arrives in the disk in molecular form; (3) the nitrogen arrives as NH3 ice; (4) most of the nitrogen arrives as NH3
gas.
2. MODEL
We use the disk chemistry model of Fogel et al. (2011)
to explore the effects of different initial abundances. We
first set the physical structure of the disk, including temperature, density, and dust properties. Next we perform
UV and X-ray radiative transfer, assuming all radiation
is from the central star. The model then calculates chemical abundances based on a network of 5903 chemical reactions and specified initial abundances. The specifics of
the model are discussed in greater detail below.
2.1. Physical Structure
We use the two-dimensional, azimuthally symmetric
disk physical structure adopted by Cleeves et al. (2013).
This model is designed to represent a ‘typical’ T-Tauri
disk based on the transition disk observations presented
by Andrews et al. (2011). The density structure is fixed
and of the form:
−1
R
R
Σg (R) = Σc
exp −
.
(1)
Rc
Rc
Here Σc and Rc are the characteristic surface density
and radius, taken to be 3.1 g cm−2 and 135 AU respectively. The disk is a settled disk, =0.1 , where is the
dust-to-gas mass ratio of dust grains in the upper disk
relative to the standard value of 0.01 (D’Alessio et al.
2006). Smaller values indicate less dust in the upper
disk and more dust in the midplane. Two types of dust
are included: small, micron size grains and larger millimeter size grains. The grain distribution is given by:
"
2 #
1 Z
(1 − f )Σ
exp −
,
(2)
ρsmall = √
2 h
2πRh
"
2 #
fΣ
1 Z
ρlarge = √
,
(3)
exp −
2 χh
2πRχh
and
h(r) = hc
R
Rc
ψ
.
(4)
The height profile given by Equation (4) is applied to
both the small dust grains and the gas, with a characteristic scale height of hc = 12 AU and ψ = 0.3. The
scale height for the large grains is smaller by a factor of
χ = 0.2. 85% of the total dust mass is in the large grains
such that f = 0.85. The dust density and temperature
distributions are shown in Figure 1.
2.2. Radiation Field
The FUV field from the central star, including Lyα
radiation, and the stellar X-ray field were generated using
a Monte Carlo radiative transfer and scattering model
as described by Bethell & Bergin (2011b,a). We adopt
the FUV spectrum to be that measured for TW Hya
(Herczeg et al. 2002, 2004). We assume a thermal X-ray
spectrum between 1 and 10 keV with an integrated X-ray
luminosity of 1030 erg s−1 , which is typical for a T Tauri
star (Glassgold et al. 1997). We then compute the X-ray
attenuation using the cross-sections of Bethell & Bergin
(2011a).
Lyα radiation contains ∼ 80% of the total FUV flux
(Herczeg et al. 2004; Bergin et al. 2003). Additionally
3
several species have photodissocation cross sections close
to Lyα. For these reasons, Lyα radiation cannot be ignored, as is the case for the weaker UV emission lines
(Fogel et al. 2011). In addition to scattering off dust
grains, Lyα photons will first isotropically scatter off of
hydrogen atoms on the top of the disk surface. This layer
scatters a fraction of the Lyα radiation more directly towards the midplane, allowing the Lyα radiation greater
penetrating power than the whole of the FUV continuum
and lines beyond Lyα (Bethell & Bergin 2011b).
2.3. Reaction Network
We use the chemical model of Fogel et al. (2011), which
is based on the gas-phase reaction network of the Ohio
State University Astrophysical Chemistry Group (Smith
et al. 2004) and modified to include the updated reaction
rates of McElroy et al. (2013). This network does not
include the expansions for reactions at high temperatures
from Harada et al. (2010). Thus the predictions for the
inner edge of the disk may change. However, in this
paper we focus on the abundances of molecules with high
volatility at radii beyond a few AU.
The chemical code is run at 74 radii with each radius
broken into 45 vertical zones. The grid spacing is logarithmic in radius and linear in angle. The chemistry in
each vertical zone is run independently, except for the
considerations needed for self-shielding, which is treated
vertically, with no mixing between zones. A pseudo twodimensional result is obtained by running the model for
many radii. The model includes photodesorption, photodissociation, freeze out, grain surface reactions, gas
phase ion and electron reactions, and cosmic ray and stellar X-ray ionization as well as self-shielding of H2 and
CO. Cosmic rays are assumed to strike the disk vertically with an unshielded ionization rate of 1.3 × 10−17
s−1 . The photodissociation rates depend on the strength
of the radiation field at a given point in the disk and
the molecule’s cross section. Grain surface reactions are
limited to the formation of H2 , H2 O, NH3 , and CH4 via
successive hydrogenation. The self-shielding and grain
surface reactions are time dependent and the chemistry
is run for 3 Myr.
2.4. Initial Conditions
We present the results from four chemical models,
each with different initial conditions as listed in Table
1. Model N uses the initial abundances of Fogel et al.
(2011), with most nitrogen originating in atomic form.
None of the initial nitrogen is in ices. Most of the oxygen is provided as either CO, nCO /nH = 1 × 10−4 , or water ice, nH2 O(gr) /nH = 2.5 × 10−4 , with a small fraction
of the oxygen in other gas phase species. These values
are for the model molecular cloud of Aikawa & Herbst
(1999), which is in good agreement with observed molecular abundances in cores (e.g. Terzieva & Herbst 1998).
In Model NH3 (gr) most of the nitrogen is in NH3 ice
and there is initially no atomic nitrogen. This is a simplification of the Maret et al. (2006) and Daranlot et al.
(2012) models which predict large NH3 ice abundances.
Model NH3 differs from Model NH3 (gr) in that it starts
with NH3 in the gas phase. This model is only viable if
the collapse of the initial molecular cloud liberates NH3
from grains. Finally, Model N2 starts with the nitrogen
primarily in N2 . As discussed above, gas phase N and N2
are not directly observable, making it difficult to observationally determine the relative gas phase abundances.
Model N2 , when compared to Model N, allows us to determine whether the partitioning between N and N2 has
an observable effect on the chemistry at later stages. We
emphasize that the variations in the initial conditions
of our models do not represent the most likely nitrogen
distribution in the disk. Rather, they are extreme examples meant to illustrate the effect the initial nitrogen
distribution has on the chemistry at later stages.
3. MODEL RESULTS
3.1. Model N
3.1.1. Radial and Vertical Structure
The following results are for a chemical time of ∼1 Myr
unless otherwise stated. The abundances of the major
nitrogen species are shown for a cross section of the disk
in Figures 2 and 3. In the cold midplane (Z = 0) the
thermal desorption rates are low, allowing many species
to freeze out onto ices. Above the midplane the ices have
evaporated and the chemistry is able to process N into
N2 as well as NH3 ice. This region corresponds to the
‘warm molecular layer’ (Aikawa et al. 2002; Bergin et al.
2007; Henning & Semenov 2013; Dutrey et al. 2014). At
R = 200 AU the warm molecular layer extends vertically
from Z ≥ 60 AU. In the upper, photon dominated region
of the disk molecules are destroyed quickly and atomic
nitrogen dominates.
Figure 4 shows the vertical structure of nitrogen carriers at a radius of 200 AU. This far from the central star,
N2 ice is only abundant close to the midplane where the
gas temperature is low, T < 20 K, and molecules are
shielded from radiation from the central star. However,
the midplane is dominated by NH3 ice. The majority
of the NH3 ice in the midplane is formed on the grains,
rather than resulting from freeze out of NH3 gas. Closer
to the star N2 ice evaporates and HCN ice, which has
a higher binding energy, is present in greater abundance
(see Figure 5).
Inside R = 200 AU chemical processing converts the
N gas into N2 in the midplane. At the disk surface N is
also able to form NH3 , CN, and HCN gas. For R < 10
AU these molecules are able to remain in the gas phase
in the surface layers, while for R > 10 AU they adsorb
onto dust grains.
The highest concentration of NH3 and NH3 ice in the
disk is in the range Z = ± 20 AU except in the outer
disk, where NH3 ice remains highly abundant at Z = ±
50 AU (Figure 2). In addition to forming on grains, NH3
is the end result of a series of ion-neutral reactions and
forms quickly in these regions. Due to its high binding
energy, NH3 ice acts as a sink, leaving little NH3 in the
gas phase. However, near the midplane there is a residual
abundance of N2 and NH3 . Cosmic ray desorption prevents N2 from completely adsorbing onto grains. Instead,
N2 remains active in the gas phase chemistry, allowing
the continued formation of NH3 . This chemistry is sensitive to the binding energies of molecules such as N2 on
grains and to the presence/absence of ionizing photons.
However, these binding energies are often uncertain and
the presence of cosmic rays in the midplane has been
called into question (Cleeves et al. 2013). This uncer-
4
tainty will be discussed in more detail in Section 3.3.
CN and HCN gas phase abundances are low in the cold
midplane region (Figure 3). These molecules are formed
via gas phase reactions and only exist in abundance in
the warm molecular layer. After forming, CN and HCN
quickly adsorb onto dust grains. Thus CN and HCN ices
also exist in the molecular layer. At R = 200 AU, HCN
ice becomes the dominant form of nitrogen at heights
between 10 and 30 AU (Figure 4). Because much of the
CN goes into forming HCN and N2 before it can freeze
out, a similar peak is not observed in CN ice.
For R > 100 AU, N2 H+ traces the midplane (Figure
3). Inside 100 AU, N2 H+ is destroyed via gas phase
reactions with CO, which does not exist in abundance in
the midplane for R > 100 AU. NO, a precursor molecule
to N2 , is most abundant in the surface layers (Z ∼ 50 −
100 AU at R = 200 AU), where the main formation and
destruction mechanisms are:
N + OH → NO + H
(5)
and
N + NO → N2 + O.
For example, irradiation of NH3 ice at 10 K can lead to
the formation of NH2 and N2 H4 while N2 becomes N3
(Gerakines et al. 1996). Especially in the warm molecular layer, which is more transparent to UV photons that
the midplane, the abundance of NH3 , N2 , and HCN ices
could decreases, corresponding to an increase in more
complex species.
Turbulent mixing would likely transport ices from the
midplane to the warmer upper regions of the disk, where
desorption would remove the molecules from grains (Furuya & Aikawa 2014). Once in the gas phase molecules
such as NH3 would be dissociated, with the nitrogen
eventually going into either N2 or N depending on the local disk temperature. Additionaly, planetesimal drift and
advection would bring ice coated grains to smaller radii
(Weidenschilling & Cuzzi 1993; Ciesla & Cuzzi 2007).
There they would evaporate, likely contributing to the
gas phase N2 abundance.
(6)
In the surface layers OH is slightly more abundant than
NO, allowing the creation of NO to outpace its destruction.
3.1.2. Radial Variation in the Midplane
Figure 5 illustrates the snow lines for nitrogen-bearing
species in the midplane. At a radius of 100 AU in the
midplane, N2 and N have evaporation temperatures of
14.8 K and 15 K respectively. These temperatures were
calculated using Eqn. 5 from Hollenbach et al. (2009)
and the binding energies in Table 1. In comparison, the
evaporation temperatures of HCN and NH3 are 38 K and
57 K. While it is fairly easy to free N and N2 from grains
in the midplane, HCN and NH3 remain locked in ices
outside of 17 AU and 5 AU respectively. This range of
evaporation temperatures results in a series of sublimation fronts. The dearth of ices at small radii does not
correspond with an increase in the gas phase abundance
of the same species. Instead, inside 150 AU the majority of the nitrogen makes its way into N2 via chemical
processing. This process is discussed in more detail in
Section 3.1.3.
Early in the chemical evolution of the disk, most of the
HCN gas in the midplane either freezes out onto grains or
is destroyed via gas phase reactions with ions. Because
of its high binding energy, it remains on grains for radii
greater than 17 AU. The same process occurs for the
NH3 and CN gas, resulting in a substantial fraction of
the total nitrogen locked in HCN and NH3 ices in the
midplane beyond 17 AU.
The resulting reservoir of moderately volatile ices could
be used to form more complex molecules, thus changing
the picture presented above. NH3 and HCN are both
needed to form aminomethanol, a precursor to glycine,
in ices via Strecker synthesis (Danger et al. 2012). The
same ices are also capable of forming hydroxyacetonitrile.
In addition hydrogenation of HCN can result in the formation of methylamine on grain surfaces (Theule et al.
2011).
Ices in the presence of UV radiation have been shown to
form more complex molecules (e.g. Bernstein et al. 2002).
3.1.3. Time Evolution
To explore time dependent behavior throughout the
disk the abundances are collapsed to radial column density plots by integrating over the vertical direction (Figure 6). These plots provides the most complete information at a given stage in addition to allowing easy examination of the time evolution of the chemistry.
At early stages, atomic N, where the majority of the
nitrogen initially resides, and N2 dominate. There is a
general evolution of N becoming N2 on fairly short time
scales via gas phase reactions with CN and NO. These
are both two step reactions:
N + CH → CN + H
(7)
N + CN → N2 + C
(8)
N + OH → NO + H
(9)
N + NO → N2 + O,
(10)
and
though other reactions can also create CN and NO. The
C and O are released when CO reacts with He+ (Bergin
et al. 2014). Beyond 50 AU these reactions primarily
take place in the warm molecular layer. Inside 50 AU
the same reactions place a majority of the initial N into
N2 early on. At t = 8.9×105 years in our model the N
gas column density still surpasses that of N2 beyond R =
200 AU. Inside of 200 AU the presence of gas phase CO
allows for more O to be present in the midplane. Some
of this O goes into OH, leading to the formation of N2
as discussed previously. The evaporation timescale increases with temperature, so as time passes larger radii
begin to be affected by evaporation. For N the evaporation timescale in the midplane at 180 AU is 1.7 × 105
years. This, in conjunction with the formation of NH3
on grains, destroys the N snow line at late stages.
Once it freezes out onto grains, N ice is quickly converted to NH3 ice. Over time this depletes the N ice
reservoir. More of the nitrogen becomes locked in NH3
and HCN ices, with HCN ices becoming the dominant
nitrogen-bearing species between 60 AU and 170 AU for
late stages. Closer to the central star HCN is more likely
to be photo-dissociated before it can freeze out onto the
grains.
5
As more of the total nitrogen becomes trapped in ices
the abundances of the molecules needed to form NH3 ,
such as NH+
4 , drop and the formation rate of gas phase
NH3 slows. This is also true for the precursors of HCN.
Thus there is little change in NH3 ice and HCN ice abundances at late stages.
3.2. Changes in Initial Conditions
In Model NH3 (gr) the initial gas phase atomic N has
been replaced with NH3 ice. Radiation from the central
star is unable to liberate the NH3 except at radii less
than ∼ 5 AU and NH3 ice remains the dominant bearer of
nitrogen for all times considered in our model (Figure 7).
Abundances of the remaining molecules are much lower
than those in Model N since most of the nitrogen remains
in NH3 ice and does not participate in the chemistry
(Figures 8 and 9).
Model NH3 places the majority of the initial nitrogen
in NH3 gas. At late stages the nitrogen partitioning is
very similar to that in Model NH3 (gr), though there are
several key differences (Figures 10-12). NH3 becomes
trapped on grains in the warm molecular layer and the
midplane early on. Before freezing out some of the gas
phase NH3 is able to react with other molecules. Because
of this there is more N2 gas, as well as HCN ice and CN
ice, in Model NH3 than in Model NH3 (gr). The formation of additional N2 depletes the NO, such that Model
NH3 has slightly lower NO abundances than those seen
in Model NH3 (gr). In the midplane the larger N2 abundance also leads to the creation of more N2 H+ beyond
300 AU when compared to Model NH3 (gr). In the surface
layers NH3 gas does not freeze out as quickly as it does
closer to the midplane. Gas phase reactions are able to
remove a larger fraction of the nitrogen from NH3 , most
of which becomes N and N2 gas.
Model N2 , where most of the nitrogen is initially in gas
phase N2 , results in a nitrogen partitioning very similar
to that of Model N (Figures 13 - 15). That the differences
are so subtle indicates that the disk is able to efficiently
transfer N to N2 , assuming there is no substantial processing of N on grains limiting the availability of atomic
N in the gas. Together, Model N and Model N2 illustrate
that if the nitrogen is delivered to the disk primarily as
either atomic or molecular nitrogen, the disk will likely
be able to produce significant amounts of N2 gas via the
reactions discussed previously.
3.3. The Effects of Binding Energies
Much of the chemistry explored in this work depends
on the amount of nitrogen available for gas phase reactions. In other words, it depends on the desorption
rates, which are extremely sensitive to the binding energies used. The residual midplane abundance of NH3 in
Figure 2 is present because the evaporation temperature
of N2 is low enough to allow gas phase N2 to exist in the
midplane. In the absence of chemical processing the gas
to ice ratio is set by balancing freeze out with thermal
and cosmic ray desorption:
n N2
nN2 (gr)
=
ν1 e−EB /T + kCR
,
ngr σvS
(11)
where nX is the number density of species X, ν1 is the
vibrational frequency of N2 bound to the grain, EB =
790 K is the binding energy of N2 (Öberg et al. 2005),
T = 16 K is the dust temperature at R = 100 AU in
the midplane, kCR = 4.37 × 10−12 s−1 is the cosmic ray
desorption rate, σ is the collisional cross section of a 0.1
micron dust grain, v is the sound speed, and S is the
sticking coefficient, assumed to be 1. At a radius of 100
AU in the midplane this gives nN2 /nN2 (gr) = 0.18. The
actual ratio for Model N is nN2 /nN2 (gr) = 0.86, indicating
that chemical processing and gas phase formation have
a non-negligible effect on the ratio.
Unfortunately it is not clear what assumptions should
be made when determining binding energies experimentally. The binding energy depends both on the species
being bound to the grain and the composition of the
grain’s surface. Commonly used surfaces include CO,
H2 O, silicates (Bergin et al. 1995), and more recently
CO2 (Cleeves et al. 2014). The binding energies of
molecules on ices can be calculated or measured in the
lab. In Model N the binding energy of N2 is 790 K (corresponding to an evaporation temperature of Tevap = 14.6
K in the midplane at 100 AU) and the binding energy of
CO is 855 K (Tevap = 16.0 K), as determined by Öberg
et al. (2005). These binding energies assume an N2 and
CO coated grain surface respectively and are appropriate for dust temperatures near 17 K. Figures 16 and 17
show the resulting chemical abundances when the binding energies for CO and N2 are both changed to 1110 K
(Tevap = 20.7 K), as is appropriate for CO2 coated grains
and dust temperatures between 25 K and 50 K (Cleeves
et al. 2014).
Changing just these two binding energies has a noticeable effect on the chemical abundances (Figures 16
and 17). The residual N2 gas near the midplane is gone,
in addition to the lower abundances of N and N2 gas
in the warm molecular layer. The abundances of most
nitrogen-bearing ices has decreased. However, much of
the nitrogen in N2 gas in Figure 2 is now trapped in N2
ice, particularly in the outer disk. With less gas phase
N2 available, the amount of NH3 gas inside of 200 AU
has also dropped.
The total amount of N2 H+ in the outer disk does not
change, though it is less concentrated in the midplane
and more abundant in the warm molecular layer compared to Model N. The outer disk contains more NO in
the high binding energy model. With less N in the gas
phase to react with, NO is not destroyed as quickly. The
differences in N2 H+ and NO are particularly interesting,
as these molecules are potentially observable.
3.4. Tracers
Many of the dominant nitrogen-bearing species, such
as N, N2 , and all ices, are not directly observable. Instead
indirect methods are needed to infer their presence. As
discussed previously the existence of NO and N2 H+ in
the midplane depends on the amount of N2 gas present.
In this section we discuss the feasibility of using NO and
N2 H+ to determine the dominant nitrogen reservoir.
We assume a disk at a distance of 140 pc inclined at
an angle of 6◦ . Emission from the N2 H+ J=4-3 transition, 372.67251 GHz, and NO (4−143 − 3134 ) transition,
350.68949 GHz, are calculated using LIME, a non-LTE
line radiation transfer code (Brinch & Hogerheijde 2010).
The N2 H+ transition was chosen based on the N2 H+
6
J=4-3 observations made by Qi et al. (2013). The NO
transition is the most readily observable transition based
on RADEX calculations (van der Tak et al. 2007)
3.4.1. Probes of the Distribution of Elemental Nitrogen
Figure 18 shows the strength of the N2 H+ (4-3) line
for our four models relative to the strongest line, while
Figure 19 shows the average emission as a function of
radius. We choose to focus on the relative line strengths
because the absolute line strength is highly dependent on
the physical model used. The strongest emission is seen
in Model N in the inner 25 AU of the disk due to a temporary increase in the local N2 H+ abundance. This is a
time dependent effect that is also seen in the other models at slightly different times. As such it should not be
used as a way to differentiate between the models. The
cause is time dependent destruction of reactive molecules
with N2 H+ . These molecules, such as CO and CH4 , are
depleted in local layers via ionization effects (Bergin et al.
2014).
Beyond R = 25 AU the strongest emission is in Model
N2 . At early times there is less atomic nitrogen available
to form NH3 on grains in Model N2 compared to Model
N and a larger fraction of the hydrogen goes into the hydrogenation of carbon on grains. With more carbon in
CH2 there is less CO available to destroy N2 H+ , leading to the stronger N2 H+ emission in Model N2 beyond
R = 170 AU. Between R = 40 AU and R = 170 AU
the emission in Model N and Model N2 is comparable.
The remaining models, Model NH3 and Model NH3 (gr),
show weaker N2 H+ emission overall. While the emission
in Model NH3 and Model NH3 (gr) is identical inside of
R = 150 AU, in the outer disk the amount of N2 H+ in
Model NH3 increases due to the increased presence of
N2 while the abundance in Model NH3 (gr) remains low.
This leads to overall weaker emission in Model NH3 (gr).
The strongest N2 H+ J=4-3 emission in Models N and N2
originates between R = 100 AU and R = 300 AU in the
midplane (Figure 19), resulting in a ring of strong N2 H+
emission, similar to that seen in TW Hya (Qi et al. 2013).
In Models NH3 and NH3 (gr) a similar, though weaker,
ring structure is seen beyond R = 300 AU.
Figure 20 illustrates the midplane abundances in Models NH3 , NH3 (gr), and N2 . Together with Figure 5 they
illustrate the gas phase N2 abundance in the N2 H+ emission region. In Model N and Model N2 , the models
with the strongest emission lines, at R = 150 AU in
the midplane, nN2 H+ /nH2 ∼ 10−10 and nN2 /nH2 ∼ 10−6 .
In comparison, for Model NH3 and Model NH3 (gr),
nN2 H+ /nH2 ∼ 10−13 and nN2 /nH2 ∼ 10−11 . When the
gas phase N2 abundance drops below nN2 /nH2 ∼ 10−6 ,
N2 H+ is no longer present. Thus, the strength of the
N2 H+ line can be used as a proxy for the midplane N2
abundance between 100 and 300 AU for an assumed ionization rate and disk structure. This is entirely consistent
with earlier work attempting to determine the N2 abundance from N2 H+ in dense cores (Womack et al. 1992).
N2 H+ has been observed in several disks (Dutrey et al.
2007; Öberg et al. 2010, 2011b). Our models suggest that
for N2 H+ to be strongly emissive there must be a significant gas phase N2 abundance. It is likely that the mere
detection of the N2 H+ (4-3) line at the level ∼ Jy at 54
pc, e.g. Qi et al. (2013), implies nN2 /nH2 > 10−6 .
The distribution of NO shows some variance between
our models. For all of our models it is present in the
surface layers. However, in Model NH3 (gr) and Model
NH3 it is also abundant in the warm molecular layer.
Model N, Model NH3 (gr) and Model NH3 all show a high
NO abundance near the midplane beyond R = 300 AU.
NO emission in strongest in Model NH3 (gr), which has
the lowest volatile nitrogen abundances. Thus, detecting
NO could indicate a depleted volatile nitrogen reservoir,
especially if the N2 H+ emission from the source is weak.
Unfortunately, because NO has an uneven number of
electrons (2 Π ground electronic state), strong rotational
transitions are replaced by a multitude of weaker lines
split by Λ doubling and hyperfine structure that is due
to the non-zero spin of the nitrogen atom (Gerin et al.
1992). As a result, detecting NO is extremely difficult.
Currently there are no NO detections towards protoplanetary disks, though circumstellar NO has been detected toward the embedded protostar NGC 1333-IRAS
4A (Yıldız et al. 2013) and it has been detected in the
dense ISM (McGonagle et al. 1990). However, our models predict the NO (4−145 − 3134 ) transition (350.68949
GHz) to be on the order of several hundred mJy for a
disk 140 pc away (Figure 21). The strongest emission
is in Model NH3 (gr), with a flux of 437 mJy. For the
full ALMA array 4.6 minutes of integration time would
be required to detect the strongest of our simulated NO
(4−145 − 3134 ) lines with a 1.400 beam at the 10 sigma
level assuming a spectral resolution of 0.3 km/s. We
again note that our models are descriptive of general effects rather than predictive of the overall flux; however,
this flux level suggests that NO may be detectable in
some systems.
3.4.2. N2 H+ as a Probe of the CO Snow Line
N2 H+ is used as a tracer of the CO snow line, since
gas phase CO destroys N2 H+ (Qi et al. 2013). Our models support this interpretation (Figures 5 and 20). The
decrease in the N2 H+ abundance between R = 200 AU
and R = 100 AU in Models N and N2 corresponds with
an increase in the CO gas phase abundance. In Models NH3 and NH3(gr) the midplane N2 H+ abundance is
much lower. While there is still an increase in the midplane abundance between R = 160 AU and R = 100 AU
in these models, the mere presence of strong N2 H+ emission at the CO snow line suggests that N2 is the main
nitrogen reservoir.
3.4.3. Surface Tracers: CN and HCN
CN and HCN are widely detected in protoplanetary
disks (e.g. Chapillon et al. 2012). Figure 22 shows the
column density ratio of CN to HCN for our four models. In Model NH3 the ratio is much larger than in the
other models inside of 5 AU due to a decrease in the
CN column density. Beyond 100 AU the column density of HCN in Model NH3 (gr) falls off, resulting in a
higher CN/HCN ratio compared to the other models.
The ratio of the simulated CN (23 − 12 ) and HCN (3-2)
line strength is 0.5 for Model N. In comparison for most
disks with detected CN and HCN emission the ratio is
between 1 and 3 (Öberg et al. 2010, 2011b). Our simulated HCN line emission is too strong. This could be due
to the specific dust structure used in this model, underestimating the highly uncertain HCN binding energy, or
7
a missing HCN processing mechanism (see discussion in
Öberg et al. 2011b).
3.5. Comparison to Cometary Abundances
Comets are thought to be indicative of the abundances
in the young solar nebula (Bockelée-Morvan 2011; Caselli
& Ceccarelli 2012). Figure 23 shows how the N2 and NH3
ice abundances in the midplane compare to the observed
abundances in comets. The figure shows the inner 50 AU
of the disk, where comets are thought to have formed
in the solar system (Mumma & Charnley 2011). The
cometary N2 value is an upper limit for Comet Halley
(Wyckoff et al. 1991). The NH3 shows the range of values detected in Comet Hale-Bopp, Comet Halley, and
Comet Hyakutake (Mumma & Charnley 2011). The N2
ice abundance relative to water is below the upper limit
for Comet Halley in all of our models, with Model N having the highest N2 to water ratio. Though our models
are not meant to be analogs for the solar nebula, Model
N reproduces the ammonia to water ratio observed in
comets, while Model N2 is at the upper limit of the observed range. This suggests either that NH3 is processed
into more refractory like material, such as part of CHON
dust grains (e.g. Jessberger & Kissel 1991) or NH3 ice is
not as easily incorporated into ices as the models predict.
In this case, at face value, these models suggest N was
delivered either as N or N2 .
4. CONCLUSIONS
We have presented four models for the initial nitrogen
abundances in protoplanetary disks. Models in which the
majority of the initial nitrogen is in gas phase atomic
N predict that N, N2 , and NH3 ice are the dominant
nitrogen-bearing species at late stages, with a significant
fraction of the nitrogen also in HCN ice. When the initial
nitrogen is instead placed in N2 gas the differences are
difficult to differentiate observationally, indicating that
the disk is able to convert gas phase N to N2 efficiently.
When the nitrogen starts as NH3 , either in the gas phase
or frozen onto grains, the majority of the N remains in
NH3 ice. Model N best matches the NH3 to H2 O ratio
in comets, suggesting that N was delivered to the solar
nebula in a highly volatile form rather than, for example,
in ices.
The presence or absence of N2 H+ in the midplane beyond the CO snow line indicates whether nitrogen is
dominated by NH3 in the midplane, with the presence
of N2 H+ correlating with the presence of N2 gas and inversely correlating with the presence of NH3 ice. N2 H+
traces the snow line in all four models, though the emission is stronger for Models N and N2 . Thus the detection of strong N2 H+ emission with a ring-like distribution
suggests a disk with a high N2 abundance. In addition,
N2 H+ emission can be used to determine the gas phase
N2 abundance in the midplane. Future sensitive observations of NO and N2 H+ combined with disk chemical
models will allow us to disentangle the nitrogen history
of protoplanetary disks.
ACKNOWLEDGMENTS
This work was supported by funding from the National Science Foundation grant AST-1008800 and AST1344133 (INSPIRE).
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9
Figure 1.
Disk model dust density and temperature structure.
Figure 2. Abundances for Model N relative to molecular hydrogen (part 1). The inset shows the inner disk. X(gr) indicates the abundance
of species X on dust grains.
10
Figure 3. Abundances for Model N relative to molecular hydrogen (part 2). The inset shows the inner disk. X(gr) indicates the abundance
of species X on dust grains.
11
Figure 4.
Abundances of nitrogen-bearing species at a radius of 200 AU after 8.9 × 105 yr for Model N.
12
Figure 5.
Radial abundance profiles at the midplane for Model N.
13
Figure 6. Column densities for the most abundant nitrogen-bearing species in our Model N. The change in scaling on the x axis at 10
AU is to better show behavior in the inner disk.
14
Figure 7.
Abundances relative to molecular hydrogen for Model NH3 (gr) (part 1). The inset shows the inner disk.
15
Figure 8.
Abundances relative to molecular hydrogen for Model NH3 (gr) (part 2). The inset shows the inner disk.
Figure 9. Column densities for the most abundant nitrogen-bearing species in Model NH3 (gr). The change in scaling on the x axis at
10 AU is to better show behavior in the inner disk.
16
Figure 10.
Abundances relative to molecular hydrogen for Model NH3 (part 1). The inset shows the inner disk.
17
Figure 11.
Abundances relative to molecular hydrogen for Model NH3 (part 2). The inset shows the inner disk.
Figure 12. Column densities for the most abundant nitrogen-bearing species in Model NH3 . The change in scaling on the x axis at 10
AU is to better show behavior in the inner disk.
18
Figure 13.
Abundances relative to molecular hydrogen for Model N2 (part 1). The inset shows the inner disk.
19
Figure 14.
Abundances relative to molecular hydrogen for Model N2 (part 2). The inset shows the inner disk.
Figure 15. Column densities for the most abundant nitrogen-bearing species in Model N2 . The change in scaling on the x axis at 10 AU
is to better show behavior in the inner disk.
20
Figure 16. Abundances relative to molecular hydrogen for Model N with and higher binding energies for CO and N2 (part 1). The inset
shows the inner disk.
21
Figure 17. Abundances relative to molecular hydrogen for Model N with higher binding energies for CO and N2 (part 2). The inset
shows the inner disk.
22
Figure 18. Model N2 H+ J = 3-2 line emission from a disk 140 pc away with an inclination angle of 6 degrees relative to the maximum
value of 10.5 Jy.
23
Figure 19. Model N2 H+ J = 3-2 line emission as a function of radius relative to the maximum value of 4 × 10−24 Jy/pixel for a disk
140 pc away.
24
Figure 20.
Midplane abundances in Models NH3 (gr), NH3 , and N2 .
25
Figure 21. Model NO line emission from a disk 140 pc away with an inclination angle of 6 degrees relative to the maximum value of
0.43 Jy. The nearby 4−145 − 3134 transition is also shown.
26
Figure 22.
Column density ratios of CN to HCN for our four models.
27
Figure 23.
Midplane abundance of N2 and NH3 ice relative to water. The horizontal lines indicate abundances in comets.
Table 1
Initial abundances relative to total H
Assumed EB (K)a
N
N2
CN
HCN
NH3
NH3 (gr)
800
790
1600
2050
3080
···
Model N
2.250 × 10−5
1.000 × 10−6
6.000 × 10−8
2.000 × 10−8
8.000 × 10−8
0
Model NH3 (gr)
0
1.000 × 10−6
6.000 × 10−8
2.000 × 10−8
8.000 × 10−8
2.250 × 10−5
Model NH3
Model N2
0
1.000 × 10−6
6.000 × 10−8
2.000 × 10−8
2.258 × 10−5
0
0
1.225 × 10−5
6.000 × 10−8
2.000 × 10−8
0
0
a Binding energies are taken from the 5th release of the UMIST Database for Astrochemistry (McElroy et al. 2013)